lim(x→∞,y→∞) x+y/x^2-xy+y^2
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lim(x→∞,y→∞)x+y/x^2-xy+y^2lim(x→∞,y→∞)x+y/x^2-xy+y^2lim(x→∞,y→∞)x+y/x^2-xy+y^2因x^2+y^2≥2|xy|,所以0≤|(x
lim(x→∞,y→∞) x+y/x^2-xy+y^2
lim(x→∞,y→∞) x+y/x^2-xy+y^2
lim(x→∞,y→∞) x+y/x^2-xy+y^2
因x^2+y^2≥2|xy|,所以
0≤|(x+y)/(x^2-xy+y^2)|
≤|x+y|/(x^2+y^2-|xy|
≤|x+y|/|xy|
≤1/|x|+1/|y|
且lim(1/|x|+1/|y|)=0
故lim[(x+y)/(x^2-xy+y^2)]=0.
0≤|(x+y)/(x^2-xy+y^2)| ≤|x+y|/(x^2+y^2-|xy| ≤|x+y|/|xy| ＝1/|x|+1/|y|
因x→∞,y→∞，lim(1/|x|+1/|y| )=0
由夹逼原理，极限是零
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